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Abstract
The d-spacing of the multilayer lamellar grating was theoretically optimized to improve the energy resolution and maintain a high efficiency. Based on the study of the growth behavior of Mo/Si multilayer on the lamellar grating under different sputtering pressures, Ar gas pressure of 1 mTorr was selected, which can fabricate the multilayer with lower roughness and a good replication of the groove shape. An absolute diffraction efficiency of 25.6% and a Cff factor of 1.79 were achieved for the -1st order of the Mo/Si lamellar multilayer grating at an energy of 1700 eV.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Synchrotron radiation and free-electron lasers (FELs) with high brilliance and photon flux have been developed to investigate the atomic and electronic structures of materials [1–3]. Particularly, “the tender x-ray region” from 1000 eV to 5000 eV [4] covers L and M absorption edges of most of the transition metals, as well as K edges of some light elements [5,6]. Many experimental techniques have been developed to study the magnetic and electronic states of nanoscale structures, such as x-ray magnetic circular dichroism (XMCD) [7,8], resonant inelastic x-ray scattering (RIXS) [9,10], and x-ray absorption fine structure (XAFS) [11,12]. However, with the increase in sensitivity and resolution of the spectroscopy methods, the challenges of monochromators with high throughput and high energy resolution are also increasing. In particular, in the low-energy range (1000–2000 eV), the typical monochromator based on single-layer grating has limited performance owing to a significant drop in diffraction efficiency [13].
Multilayer gratings, which meet both the grating diffraction and multilayer Bragg diffraction conditions, can achieve high diffraction efficiency compared to single-layer coated gratings. To achieve high diffraction efficiency, different multilayer gratings have been developed and characterized for tender x-ray applications. For the multilayer blazed gratings, Voronov et al. [14–17] optimized the process of multilayer deposition in order to weaken the smoothing effect on the groove shape and measured approximately 25% efficiency with the W/B4C multilayer blazed grating at a wavelength of approximately 1 nm. Senf et al. [18] and Sokolov and Huang et al. [19] optimized the structure parameters to match the Cr/C multilayer to the blazed grating and recorded an efficiency of 35% at 2 keV and 60% at 3.1 keV and 4.1 keV. However, limits in the manufacturing techniques make it very difficult to create a blazed grating with an accurate blaze angle and a supersmooth surface over a large area [20], which affects the diffraction efficiency of optics and limits its wide application. Lamellar gratings are easier to fabricate and can be widely applied in beamlines. Polack et al. [21] and Choueikani et al. [22] developed Mo2C/B4C multilayer lamellar gratings for monochromators in the tender x-ray region, and the optics were installed in the DEIMOS beamline at SOLEIL, with a measured diffraction efficiency of approximately 23% at 1700 eV [6].
In addition to diffraction efficiency, energy resolution is another extremely important parameter of monochromators which also needs to be considered. A low energy resolution monochromator is unable to obtain sufficiently separated spectra, which is extremely unfavorable for characterizing the atomic and electronic structures of materials. Multilayer gratings, working as a high-flux monochromator, operate at a higher grazing incidence compared with single-layer gratings, resulting in low dispersion power and Cff factor. There are some methods to increase the spectral resolution, such as reducing the grating period. The method of increasing the multilayer d-spacing is more a complimentary to other methods, which does not change the grating structure. Huang and Kozhevnikov et al. [4] theoretically proposed that increasing the d-spacing can improve the energy resolution of multilayer gratings. However, for multilayer lamellar gratings, the method requires further verification and experimental optimization to balance the diffraction efficiency and energy resolution. In addition, there have been few experiments to study the smoothing effect of the deposition process on the lamellar grating to achieve perfect groove replication and low interface roughness simultaneously.
In this study, we designed the optimal structure of a multilayer lamellar grating to balance the diffraction efficiency and energy resolution, and experimentally achieved the perfect replication of a groove with a smoothing multilayer. The changes in the diffraction efficiency and energy resolution with the d-spacing of the multilayer were analyzed in the design of the Mo/Si multilayer lamellar grating with a line density of 1800 L/mm and experimentally demonstrated in the energy region of 1000–1700 eV. An absolute diffraction efficiency of 25.6% and a Cff factor of 1.80 were achieved for the −1st order of the Mo/Si lamellar multilayer grating at an energy of approximately 1700 eV.
2. Design and simulation of multilayer lamellar gratings
A perfect multilayer lamellar profile grating coated with alternate thin layers of the two materials is shown in Fig. 1. The form is a two-dimensional periodic structure where the two directional periods are very different, a few nanometers in depth (z direction) but several hundreds of nanometers in the surface plane (x direction). The multilayer grating (MLG) should satisfy both the grating equation and Bragg condition to achieve the maximum diffraction efficiency. When the grating has a given photon energy, diffraction in a given order occurs only for a specific incidence angle α and diffraction angle β, which are determined by the period of the grating p and d-spacing of multilayer d. In particular, we proved in previous work that when d-spacing of the multilayer is twice the groove depth, the model reaches the maximum diffraction efficiency [23].
The theoretical energy resolution of a monochromator is significantly affected by the fixed-focus factor Cff = sinβ/sinα [4,19,24,25]. The change in the incidence and diffraction angles (β, α) depends on the multilayer grating structure (p, d). More specific and detailed parameters can be calculated numerically using rigorous coupled wave analysis (RCWA) [26].
In the energy region of 1000–1700 eV, the multilayer material combination of Mo/Si could provide higher reflectance compared with the combinations of W/Si, Cr/C, etc.. Therefore, the Mo/Si multilayer was selected to match the lamellar grating. First, we calculated the model, in which the grating period was p = 555 nm (1800 L/mm), the d-spacing of the multilayer was d = 5 nm, and the best groove depth was half the d-spacing, and a saturated number of bilayers (N = 50) of the multilayer was used to achieve maximum efficiency, and the thickness ratio of Mo to the d-spacing was 0.4. The ratio of the groove to the entire cycle was set to 0.7, which is close to the actual groove shape. The diffraction efficiency for the −1st order at an energy of 1700 eV could reach 32.0%, but the Cff factor was only 1.25, which represents a very low energy resolution.
Increasing the d-spacing of the multilayer is expected to improve the energy resolution and Cff factor of the MLG. In this case, we investigated the change in the diffraction efficiency and the Cff factor as the d-spacing of the multilayer. The trend for the −1st order at the energy of 1700 eV is shown in Fig. 2, where the groove depth is always half of the d-spacing and the grating line density is 1800 L/mm. The results show that the Cff factor increases almost linearly with an increase in d-spacing, while the diffraction efficiency decreases owing to the increase in radiation absorption and shadow regions. The purpose of optimization is to increase the Cff value as much as possible, while maintaining a diffraction efficiency of more than 90% from the value of d = 5 nm. As a result, the case of d = 9.5 nm is the best choice, in which the diffraction efficiency is 29.5% and the Cff factor is 1.88, which is increased by about 50% relative to the case of d = 5 nm. For a typical Au single-layer grating with a line density of 1800 L/mm, the calculated Cff factor is approximately 2.3, but the diffraction efficiency is only approximately 6%, which exceeds the tolerance for diffraction efficiency loss. Therefore, we selected the case of d = 9.5 nm for the experimental demonstration, which is more beneficial for greatly improving the energy resolution as large as possible and keeping the diffraction efficiency.
Fig. 2. The change of diffraction efficiency and the Cff factor with the d-spacing of Mo/Si multilayer lamellar grating for the −1st order at the energy of 1700 eV.
3. Fabrication and structural characterization of the samples
Mo/Si multilayer gratings and their reference multilayer mirror samples were fabricated using a direct-current (DC) magnetron sputtering technique. The diameter of the target source is about 4 inches. The substrate stays directly above the sputtering source during deposition of each layer and the thickness of the films depends on time. In addition, the sample does not self-rotate during the sputtering process. Atomic fluxes under different pressures have different kinetic energies, which cause different smoothing effects in the film growth process. Based on the work of Voronov et al. [15], we studied the smoothing effects of the deposition process sputtered at Ar gas pressures of 1 and 3 mTorr to determine the best sputtering pressure. AFM results indicate the grating groove depth is about 5.95nm. Based on optimization results, the best d-spacing of multilayer is about 9.5 nm instead of 12 nm, which could be due to the deflection of incident beam to total reflection area and the enhancement of zero-order diffraction efficiency. Therefore, we selected d = 9.5 nm as the preparation target. The ratio of the Mo layer to the total thickness was 0.4, and the saturated layer number was 20.
After fabrication, the reference multilayer mirror samples were characterized by grazing incident x-ray reflection (GIXRR) on a high-resolution x-ray diffractometer (D1 system, Bede Inc.). The surface roughness of the multilayer mirrors and the groove shape of the multilayer gratings were characterized using atomic force microscopy (AFM) on a Bruker Dimension Icon system in tapping mode. The scan sizes of the multilayer mirrors and multilayer gratings were 2 µm × 2 µm and 5 µm × 5 µm, respectively, and the scan area consisted of 256 × 256 pixels. In addition, the cross-sectional image of the multilayer grating sputtered at an Ar gas pressure of 1 mTorr was measured by high-resolution transmission electron microscopy (HRTEM). TEM measurements were performed using FEI Talos F200X equipment in Materials Analysis Technology Inc.
Figures 3(a) and 3(b) present the surface morphology of Mo/Si multilayer mirrors sputtered at Ar gas pressure of 1 and 3 mTorr, respectively. Compared with the sample sputtered at 1 mTorr, the sample sputtered at 3 mTorr has more fine particles on the surface. One-dimensional power spectral density (PSD) along the horizontal direction was calculated from AFM images, shown in Fig. 3(c), which provides a representation of the amplitude of surface roughness as a function of the spatial frequency. As for the PSD of the sample sputtered at 1 mTorr, one prominent feature is the significant drop in the spatial frequency range (10 µm−1–30 µm−1) compared to the sample sputtered at 3 mTorr, which indicates that the deposition process with lower sputtered pressure could provide a more effective relaxation in this spatial frequency range. The surface root-mean-square (RMS) was calculated by integrating the PSD curve. The surface roughness value is 0.130 nm for the sample sputtered at 1 mTorr, and 0.169 nm for the sample sputtered at 3 mTorr, which is consistent with previous studies that higher sputtered pressure results in higher roughness [15]. The results indicated that the deposition process with 1 mTorr sputtered pressure could promote the surface diffusion along the interfaces and provide smoother interfaces.
Fig. 3. The AFM surface morphology of the Mo/Si multilayer sputtered at Ar gas pressures of a) 1 mTorr, and b) 3 mTorr, respectively. c) Comparison of PSD functions calculated for the top surface of Mo/Si multilayers.
The AFM images of the multilayer gratings sputtered under Ar gas pressures of 1 and 3 mTorr are shown in Figs. 4(b) and 4(c), respectively, while the topography of the grating substrate is shown in Fig. 4(a). The groove profiles of the samples are presented in Fig. 4(d). It can be seen that the grating period is approximately 555 nm (∼1800 L/mm), and the ratio of the groove to the entire cycle is approximately 0.62. After deposition, the sidewall angle of the groove sputtered at 1 mTorr was slightly smaller than that of the grating substrate. More detailed changes are shown in the TEM results. The PSD spectra of the samples, shown in Fig. 4(e), consist of a number of peaks that correspond to harmonics of the Fourier transform of the rectangular profile. There is no significant decay of higher-order harmonics, indicating that the deposition process, whether at a sputtering pressure of 1 mTorr or 3 mTorr, did not evidently smooth the groove shape. Meanwhile, the PSD feature of the sample sputtered at 1 mTorr is lower at high spatial frequencies (>20 µm−1), which indicates that there is more effective relaxation at high spatial frequencies. This is consistent with the result of the multilayer sample. Therefore, the best sputtering pressure was 1 mTorr, in which multilayer gratings had lower roughness while maintaining great replication of the groove shape.
Fig. 4. The AFM surface morphology of a) lamellar grating substrate and sputtered with Mo/Si multilayers at Ar gas pressures of b) 1 mTorr, and c) 3 mTorr, respectively. d) Comparison of the groove profiles of samples. e) Comparison of PSD functions calculated for the top surface of substrate and MLGs.
Figure 5(a) shows TEM images of the whole cross-section of the multilayer grating sputtered at 1 mTorr, where the Mo layers appear dark and the Si layers appear bright. The MLG with the optimized Mo/Si multilayer provided a great conformal replication of the lamellar grooves of the substrate. In addition, it can be observed that the grooves shift slightly to the left as the film thickness increases, which may be attributed to a slight deviation in the average direction of atomic flux from the surface normal of the substrate [16]. TEM images with higher resolution are measured to present the evolution of grating grooves. Figures 5(b) and 5(c) show the structure of the sidewalls on the left and right sides of the top part, while Figs. 5(d) and 5(e) show the structure of the sidewalls on the left and right sides of the bottom part, respectively. The sidewall angle of the first layer, αd ≈ 9.7°and αe ≈ 8.7°, is significantly smaller than the slope angle of the grating substrate (α0 ≈ 12.4°). The thickness of the sidewall was also smaller than that of the flat area. When atoms reach the surface of the substrate, the surface migration rate in the sidewall is faster, decreasing the deposition rate and resulting in a slower slope and thinner layer [27–29]. The deviation of the particle flow from the surface normal of the substrate leads to differences in the layer growth rate and surface migration on both sides of the sidewalls, resulting in different sidewall angles. As the film layer increases in the top part, there is no obvious change in the angles of the slope, with αb ≈ 9.0°and αc ≈ 7.9°. The results indicate that the deposition process of the first layer has the greatest impact on the groove shape, while the subsequent layer maintains the replication of the groove shape of the first layer. Combining the results of AFM and TEM, the layer growth on the grating with a period of approximately 555 nm does not cause significant smoothing. In our case, the reduction in the simulated diffraction efficiency is less than 1% while slope angle of grating model changed from 12.5° to 8°.
Fig. 5. TEM image of a) the whole cross-section of MLG sputtered at 1 mTorr and HRTEM images of structure of the slopes on the b) left and c) right sides of the top part, and on the d) left and e) right sides of the bottom part, respectively.
4. Tender x-ray measurements
The optical performance of the Mo/Si multilayer lamellar gratings and reference multilayer mirror for the energy range of 1000–1700eV was measured with Optics Beamline PM-1 at the BESSY-II facility. The normal incident beam size illuminated on the sample was 0.35 × 0.2 mm2 (v × h) at PM-1, and the beam stability on the Optics beamline was better than 0.1%, and each sample structure was aligned individually with a high accuracy in six degrees of freedom [30]. For the reflectivity measurement, detectors with an aperture of 4 × 4 mm2 were used, which was large enough to collect the specular reflected beam and most of the scattered beam. For the detector scans (in-plane scans) of the dispersion patterns, detectors with slit apertures of 0.14 × 4 mm2 (v × h) were used.
To verify the influence of sputtering pressure on the optical properties of the multilayers, the reflectance of the Mo/Si multilayers was measured. Figure 6 shows the reflectance curves of the multilayers sputtered at an Ar gas pressure of 1 mTorr and 3 mTorr as a function of photon energy around 1700 eV. The center energy peak position shifts owing to the thickness deviation. The -1st order peak reflectance of the sample sputtered at an Ar gas pressure of 1 mTorr was 56.2%, which is very close to the theoretical value of 60.7% for an ideal layer structure (perfect interface) performed with IMD software. The peak reflectance of the sample sputtered at an Ar gas pressure of 3 mTorr was as low as 52.7%. The reflectance curves were fitted with a model of four layers in the period, i.e. a Mo/Mo5Si3/Si/MoSi2 layer [31,32]. The detailed fit parameters are listed in Table 1. It can be seen that the layer thickness has a deviation, but the average interface of the sample sputtered at 1 mTorr is smaller. The results indicate that the sample sputtered at a lower Ar gas pressure has a smoother interface and higher reflectance, which is consistent with the previous structural characterization results.
Fig. 6. The measured and fitted reflectance curves of Mo/Si multilayers sputtered at 1 mTorr and 3 mTorr as a function of photon energy around 1700 eV.
Table 1. Parameters of fitted reflectance curves of Mo/Si multilayers sputtered in 1 mTorr and 3 mTorr shown in Fig. 6.
Measurements of the diffraction efficiency of the Mo/Si multilayer lamellar grating sputtered at an Ar gas pressure of 1 mTorr were performed. Figure 7 shows the efficiency curves of the -1st order of the sample as a function of photon energy selected in the tender x-ray region of 1000–1700eV. At each energy point, the most optimal incidence angle is determined by angular scanning, and the detector rotates with the energy according to the grating equation to record the diffraction efficiency. At the same time, the simulated peak diffraction efficiency value of the ideal model, in which the ideal layer structure is matched with the groove profile extracted from the TEM image, is also shown in the figure. The diffraction efficiency of the grating increased with energy and followed the same trend as the simulated results. The measured efficiency is slightly lower than the theoretical calculation value. The grating working in the −1st order with a grazing incident angle of 1.95° achieves an efficiency (E−1st) of 25.8% at 1700 eV, which is lower than the calculated value of 31.2%. To evaluate the performance of multilayer film gratings, the ratio η = E-1st/RMLs can be defined as the relative efficiency of the optics. In this case, the ideal relative efficiency is ηi = 0.51, while the measured ratio ηm = 0.46. A structure factor Ω = (ηm / ηi) ×100% = 90% can then be obtained, representing the degree of the ideal model achieved by the experiment. Interface defects and groove shape changes are factors that prevent the measured efficiency of multilayer gratings from fully reaching the design value. Furthermore, the estimated diffraction efficiency curve, which is obtained from the simulated results with structure factor and roughness factor, i.e. Eestimated = Esim × Ω × (Rm/Ri), is also shown in the figure. The estimated curve was mostly consistent with the measured results, indicating the feasibility of the evaluation method. It is noteworthy that the low-energy part of each measured curve is lower than the estimated results. The reduction of measured efficiency could be caused by the fast degradation of phase matching when moving away from the resonance energy and stronger absorption in the low energy region.
Fig. 7. The measured and estimated diffraction efficiency curves (squares/lines) of the −1st order of MLG as a function of photon energy selected in the tender x-ray region of 1000–1700eV. Circles indicate the simulated peak diffraction efficiency value of the ideal model. Incidence angle at each energy point is also marked above the curve.
Figure 8 shows the Cff factors of the Mo/Si multilayer lamellar grating sputtered at an Ar gas pressure of 1 mTorr as a function of photon energy. The measured Cff factors were determined from the measured incident angle and diffraction angle, while the theoretical Cff factors were calculated from the simulated angle. As the energy increases, the Cff factor also increases, indicating that the Mo/Si multilayer lamellar grating can obtain a higher energy resolution. In this case, the optic could work with Cff = 1.79 and a photon energy of 1700 eV, which is close to the theoretical value of 1.81.
Fig. 8. The Cff factors of MLG as a function of photon energy: measured results (point-line), and simulation (dashed-dotted line).
To evaluate the angular dispersion of the sample, two-dimensional scans of both the photon energy and diffraction angle around the resonant conditions of the −1st order are presented in Fig. 9. Under a fixed incidence of 1.95°, the detector scans every 5 eV to record light intensity changes in the energy region of 1600–1850 eV. The angular position for peak efficiency at each energy was determined, and is connected by a dashed line within the central high-efficiency area in the figure. The slope of the line is equal to Δθ/ΔE, representing the angular dispersion of the optics [33]. For the Mo/Si multilayer lamellar grating measured at an incidence angle of 1.95°, the angular dispersion was about 0.00078°/eV in the energy range of 1620–1780 eV. This is consistent with the theoretical value of a nanograting with a 555 nm period (1800 L/mm) derived by the grating equation. In the case of d = 5 nm, the calculated angular dispersion is about 0.00055°/eV. Therefore, the angular dispersion could be increased by about 40% through increasing the d-spacing of multilayer. Compared with the Au single-layer grating, in which the calculated angular dispersion is about 0.00088°/eV, the diffraction efficiency of the multilayer grating with d-spacing of 9.5 nm is increased by about 5 times, while the angular dispersion is reduced by about 10%. The results indicated the method is favorable that improving the spectral resolution of grating optics by increasing the d-spacing of multilayer.
Fig. 9. Two-dimensional diffraction measurements as a function of diffraction angle and photon energy of the −1st order of the Mo/Si MLG at an incident angle of 1.95°.
The Mo/Si multilayer lamellar grating can also achieve extremely low transmission of higher diffraction orders, providing good suppression of higher harmonics in a beamline. Figure 10 shows the peak efficiency as a function of the detector scan angle, with a fixed incidence angle of 5.0°, photon energy of 800 eV, and double energy of 1600 eV. The 0th orders for both 800 and 1600 eV are visible at the same angle because the 0th order diffraction is equivalent to specular reflection; that is, the diffraction angle is equal to twice the incident angle, regardless of the photon energy. The −1st order for 800 eV appears at 11.53°, which corresponds to the 2nd order of 1600 eV. It can be seen that the transmission of the 2nd order of 1600 eV is three orders of magnitude lower than the −1st order of 800 eV. The low transmission of the 2nd order at high energy points is due to the mismatch between the diffraction angle of the grating and the second-order Bragg diffraction angle of the multilayers, which is caused by the refraction effects of x-rays propagating through the layers [18]. The performance of the suppression of higher harmonics is the same as the results of the previously reported Cr/C multilayer blazed grating [18].
Fig. 10. Detector scan for the energy 0.8 keV (black) and the double energy 1.6 keV (red). The incidence angle was fixed at 5.0°.
5. Conclusions
The design and experimental optimization of the Mo/Si multilayer lamellar grating were investigated to balance the high diffraction efficiency and energy resolution in the tender x-ray region of 1000–1700 eV. Through accurate numerical simulations, the effect of d-spacing on the diffraction efficiency and energy resolution was explored. In the experiments, Mo/Si multilayer lamellar gratings with a line density of 1800 L/mm and reference multilayer samples were fabricated using a direct current (DC) magnetron sputtering technique. The results indicate that the Mo/Si multilayer lamellar grating sputtered at an Ar gas pressure of 1 mTorr had lower roughness while maintaining perfect replication of the groove shape. The optical performance of the Mo/Si multilayer lamellar gratings and reference multilayer mirror for the energy range of 1000–1700 eV was measured at the Optics Beamline at BESSY-II. An absolute diffraction efficiency of 25.6% and a Cff factor of 1.80 were achieved for the −1st order of the Mo/Si lamellar multilayer grating at an energy of approximately 1700 eV. In addition, the optics also exhibit good performance in terms of angular dispersion and suppression of higher harmonics. The investigation verified that it is feasible to improve the energy resolution and maintain the high diffraction efficiency of multilayer lamellar gratings by increasing the d-spacing of the multilayer. This work can provide valuable guidance for the application of multilayer grating monochromators in beamlines.
Funding
National Natural Science Foundation of China (NSFC) (61621001, U1732268, 12075170); Shanghai Rising-Star Program (19QA1409200); Major Projects of Science and Technology Commission of Shanghai (17JC1400800).
Disclosures
The authors declare that there are no conflicts of interest.
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